Select all overlapping vertices
Ok, here the script that adds button with such function to "Select all by trait menu". Feel free to improve

bl_info = {
    "name": "Select Doubles",
    "author": "Lambdadelta",
    "version": (1, 0),
    "blender": (2, 78, 0),
    "location": "(Edit Mode) Select &gt; Select All by Trait",
    "description": "Select all duplicate vertices.",
    "warning": "",
    "wiki_url": "http://blender.stackexchange.com/questions/68326/select-all-overlapping-vertices",
    "category": "Mesh",
    }

import bmesh
import bpy
from mathutils import Vector, kdtree

def select_duplicate_vertices(context, distance):
    obj = bpy.context.object
    me = obj.data
    bm = bmesh.from_edit_mesh(me)
    verts = bm.verts
    verts.ensure_lookup_table()

    # Create a kd-tree from a mesh
    size = len(verts)
    kd = kdtree.KDTree(size)
    for i, vtx in enumerate(verts):
        kd.insert(vtx.co, i)
    kd.balance()

    # Deselect all
    bpy.ops.mesh.select_all(action = 'DESELECT')

    # Select duplicate vertices
    for i, vtx in enumerate(verts):
        vtx_group = []
        for (co, index, dist) in kd.find_range(vtx.co, distance):
            vtx_group.append(index)
        if len(vtx_group) &gt; 1:
            #print(vtx_group)
            for index in vtx_group:
                verts[index].select = True

    # Switch to vertex select
    bpy.ops.mesh.select_mode(use_extend=False, use_expand=False, type='VERT')

    # Show the updates in the viewport
    bmesh.update_edit_mesh(me, False)


class SelectDoubles(bpy.types.Operator):
    """Select duplicate vertices"""
    bl_idname = 'mesh.select_doubles'
    bl_label = 'Select Doubles'
    bl_options = {'REGISTER', 'UNDO'}

    distance = bpy.props.FloatProperty(                        
        name = "Distance",    
        subtype='DISTANCE',          
        default = 0.001,
        min = 0.0,
        max = 50.0,
        description = "Minimum distance between elements to select.",
        unit='LENGTH'
        )

    def execute(self, context):
        select_duplicate_vertices(context, self.distance)
        return {'FINISHED'}

    def invoke(self, context, event) :
        select_duplicate_vertices(context, self.distance)
        return {"FINISHED"}

def menu_func(self, context):
    self.layout.operator(SelectDoubles.bl_idname, text="Select Doubles")

def register():
   bpy.utils.register_class(SelectDoubles)
   bpy.types.VIEW3D_MT_edit_mesh_select_by_trait.append(menu_func)

def unregister():
    bpy.utils.unregister_class(SelectDoubles)
    bpy.types.VIEW3D_MT_edit_mesh_select_by_trait.remove(menu_func)

if __name__ == "__main__":
    register()